The only way I can possible think of, how this is possible is if the glow plugs were upgraded to pencil style from loop and the ground strap was connected to the last pencil plug. This would in theory add 12v to the block.

I would personally remove the battery and battery box, and get a better view at the wires connected to the solenoid and confirm everything is hooked up properly and none of the wires touching.

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I'll take a look at that too; the plugs are the upgraded pencil-style. I don't recall if the PO(s) removed that old GP ground or not.

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- 1979 W123 240D 4-speed, 390k miles

If my eyes are not dodgy in reading

Im seeing that someone connected the positive thick battery wire to the starter to an engine ground - this will cause massive sparks/welding/fire as you are dead shorting the battery.

By connecting the starter small and big wire terminals together you are bypassing everything and the starter motor is energizing, which is proves that the ground is good - that motor sucks north of 400 amps when turning that high CR 4 cyl diesel. A bad ground would cause the motor not to operate at all in that case.

What you have is low amps from the key/NSS to the starter solenoid, you can test this by using a sealed beam headlamp or a working H4 bulb with both elements connected together combined to give a load of about 10 amps. If you test that the solenoid wire can immediately illuminate the beam to full bright your system is good, if its faint or orange glow, resolve it.

You might also want to add a starter relay (aka hot start relay) to boost the system.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)

So, just to be clear, the main wire from the battery comes into the top terminal, and the wire to the alternator also connects to that top terminal. There are two small wires; a purple one which I assume is the direct line to the starter, and a bypass line for the glow relay. Nothing connects to the bottom (ground) large terminal.

Right...?

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- 1979 W123 240D 4-speed, 390k miles

If the AAA guy grounded the lower solenoid terminal that has a braided wire going into the starter windings then your starter is a bit corroded internally or the brush pack holding screws are stripped or corroded. They are the ground.

The solenoid takes it ground from inside the starter windings for the pull coil which then bridges the high current contacts in the solenoid for the motor to work.

You need to remove that starter and overhaul it.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)

The Nut and Strap that are between the Starter Housing and the Solenoid is another Posative connection. When the Solenoid Moves it connects the large + Termnial with that lower Large Termainl and that is what causes the Starter to rotate.

I don't remember if this is a Pic of a Delco Starter or a Mercedes Starter but they both have similar parts and work the same.
The Red arrow point to the 2 High Amperage Contacts that the Solenoid connects to each other when the Sonlenoid is activated.

Attached Thumbnails

 

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84 300D, 82 Volvo 244Gl Diesel

That looks like a w123 starter!

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Grumpy Old Diesel Owners Club group

I no longer question authority, I annoy authority. More effect, less effort....

1967 230-6 auto parts car. rust bucket.
1980 300D now parts car 800k miles
1984 300D 500k miles
1987 250td 160k miles English import
2001 jeep turbo diesel 130k miles
1998 jeep tdi ~ followed me home. Needs a turbo.
1968 Ford F750 truck. 6-354 diesel conversion.
Other toys ~J.D.,Cat & GM ~ mainly earth moving